指出解线性方程组不能用初等列变换的原因。证明了利用列交换(初等列变换)解齐次线性方程组的相关定理,并通过例题进行了检验。该方法对行简化的阶梯形矩阵的左上角是或不是单位矩阵类型的方程组,能有效、方便的求出基础解系和通解。
This paper points out the reason why the elementary column transform can' t be used in solving homogeneous linear equations. Some theorem related to the solution of linear equations using the column transform has been proved and verified by examples. This method can find the basic solution system and the general solution of equations effectively and easily, whether the upper left comer of the echelon matrix which was simplified coefficient matrix by row transform is unit matrix or not.